pw42, now that I have you on the right track, visit your local dealer and ask about the kit that solves this issue. You can just split it but the shaft might walk out again. Get your parts kit and ask him if he can give you a few tips on how it comes apart and goes together. It's not all that complicated, but it has to be split at the bell housing and then once again I think at the next casing. Might as well put the new improved parts in it. Good for you for being willing to tackle a project like this.
If you are just going to stick it back together with no new parts, then I'd scratch my head for a while and see if you can make a custom set of pliers to grab the shaft through the hole to push it back in place. I never went that route as we replaced with the new parts. But I'd think it may be possible to pull this off.